Simplify the following expression: $\dfrac{25n^2}{5n^5}$ You can assume $n \neq 0$.
Explanation: $ \dfrac{25n^2}{5n^5} = \dfrac{25}{5} \cdot \dfrac{n^2}{n^5} $ To simplify $\frac{25}{5}$ , find the greatest common factor (GCD) of $25$ and $5$ $25 = 5 \cdot 5$ $5 = 5$ $ \mbox{GCD}(25, 5) = 5 $ $ \dfrac{25}{5} \cdot \dfrac{n^2}{n^5} = \dfrac{5 \cdot 5}{5 \cdot 1} \cdot \dfrac{n^2}{n^5} $ $\phantom{ \dfrac{25}{5} \cdot \dfrac{2}{5}} = 5 \cdot \dfrac{n^2}{n^5} $ $ \dfrac{n^2}{n^5} = \dfrac{n \cdot n}{n \cdot n \cdot n \cdot n \cdot n} = \dfrac{1}{n^3} $ $ 5 \cdot \dfrac{1}{n^3} = \dfrac{5}{n^3} $